Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $7062.5
Rate of Simple Interest (R) = 5%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$7062.5 = P (1 + 5% × 5)
⇒ $7062.5 = P (1 + 5/100 × 5)
⇒ $7062.5 = P (1 + 5 × 5/100)
⇒ $7062.5 = P (1 + 25/100)
⇒ $7062.5 = P (100 + 25/100)
⇒ $7062.5 = P × 125/100
⇒ P × 125/100 = $7062.5
⇒ P = 7062.5/125/100
⇒ P = 7062.5 × 100/125
⇒ P = 7062.5 × 100/125
⇒ P = 706250/125
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7062.5, then the Principal = 100/125 × 7062.5
= 100 × 7062.5/125
= 706250/125
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(6) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.